Let us investigate the multiphoton excitations of Fermi-Dirac sea in the
gapped bilayer graphene in nonadiabatic regime. In accordance with the
microscopic nonlinear quantum theory of \(AB\)  stacked gapped bilayer
graphene, the low-energy excitations \(\left|\mathcal {E}_{\sigma }\right|<\gamma _{1}\simeq 0.39\)  \(\mathrm {eV}\)  in the immediate
vicinity of the Dirac points \(K_{\zeta }\)  (valley quantum number \(\zeta =\pm 1\) ) one can describe by the effective single particle Hamiltonian [1]}, [2]}, [3]}:
\(\widehat{H}_{\zeta }=\left(\begin{array}{cc}\frac{U}{2} & h_{\zeta }^{\ast }\left( \mathbf {p}\right) \\h_{\zeta }\left( \mathbf {p}\right) & -\frac{U}{2}\end{array}\right) . \) 
